Global ETD Search
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Showing 1 to 5 of 5 for “"polyominoes"”.
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Tiling with Polyominoes, Polycubes, and Rectangles
… we study the hierarchical structure of the 2-d polyominoes. We introduce a new infinite family of polyominoes which we prove tiles a strip. We discuss applications of algebra to tiling. We discuss the algorithmic decidability of tiling the infinite plane Z x Z given a finite set of polyominoes. …
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Geometric and algebraic properties of polyomino tilings
… study tilings of regions on the square grid by polyominoes. A polyomino is any connected shape formed from a union of grid cells, and a tiling of a region is a collection of polyominoes lying in the region such that each square is covered exactly once. In particular, we focus on two main themes: …
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Closed-Loop Control of Mesoscale Magnetic Robots Using a Global Magnetic Field
… magnetically connected structures of MMCs are polyominoes in 2D and polycubes in 3D. MMCs represent progress toward a mesoscale manufacturing method controllable by an external force field that combines the precision of modules, the reusability of Legos, and the self-assembly of DNA. The …
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Development of Atomistic Potentials for Silicate Materials and Coarse-Grained Simulation of Self-Assembly at Surfaces
… of shape on self-assembly and thermodynamics for polyominoes and tetrominoes were examined. Many interesting results were observed, including complex clustering, non-ideal mixing, and phase transitions. In both parts, computational efficiency and performance were important goals, and this was …
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Modelling the evolution of biological complexity with a two-dimensional lattice self-assembly process
… in evolution. Transitions between certain polyominoes are strongly forbidden when interaction strengths are misaligned. The third aspect focuses on genetic duplication, an evolutionary event observed in organisms across all taxa. Through polyomino evolutions, a duplication-heteromerisation …